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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Results (1-50 of 237 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
130.2.a.a	$130$	$2$	130.a	1.a	$1$	$1$	$1$	$1.038$	$\Q$	None	✓	$1$	$1$	$-1$	$-2$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-4q^{7}+\cdots$
130.2.a.b	$130$	$2$	130.a	1.a	$1$	$1$	$1$	$1.038$	$\Q$	None	✓	$1$	$0$	$1$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots$
130.2.a.c	$130$	$2$	130.a	1.a	$1$	$1$	$1$	$1.038$	$\Q$	None	✓	$1$	$0$	$1$	$2$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots$
130.2.b.a	$130$	$2$	130.b	5.b	$2$	$6$	$6$	$1.038$	6.0.3534400.1	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{2}+(\beta _{3}-\beta _{4})q^{3}-q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots$
130.2.c.a	$130$	$2$	130.c	65.d	$2$	$4$	$4$	$1.038$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$-4$	$0$	$3$	$2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{3})q^{5}+\beta _{2}q^{6}+\cdots$
130.2.c.b	$130$	$2$	130.c	65.d	$2$	$4$	$4$	$1.038$	$\Q(\sqrt{-3}, \sqrt{-11})$	None		$2$	$0$	$4$	$0$	$-3$	$-2$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{3})q^{5}+\cdots$
130.2.d.a	$130$	$2$	130.d	13.b	$2$	$2$	$2$	$1.038$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$4$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{2}+2q^{3}-q^{4}+iq^{5}+2iq^{6}+\cdots$
130.2.e.a	$130$	$2$	130.e	13.c	$3$	$2$	$1$	$1.038$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$-1$	$0$	$2$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+3\zeta_{6}q^{7}+\cdots$
130.2.e.b	$130$	$2$	130.e	13.c	$3$	$2$	$1$	$1.038$	$\Q(\sqrt{-3}) $	None		$2$	$0$	$1$	$2$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+(2-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$
130.2.e.c	$130$	$2$	130.e	13.c	$3$	$4$	$2$	$1.038$	$\Q(\sqrt{-3}, \sqrt{10})$	None		$2$	$0$	$-2$	$0$	$-4$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
130.2.e.d	$130$	$2$	130.e	13.c	$3$	$4$	$2$	$1.038$	$\Q(\zeta_{12})$	None		$2$	$0$	$2$	$-2$	$4$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots$
130.2.g.a	$130$	$2$	130.g	65.k	$4$	$2$	$1$	$1.038$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$-2$	$-4$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(-2-2i)q^{3}+q^{4}+(-2-i)q^{5}+\cdots$
130.2.g.b	$130$	$2$	130.g	65.k	$4$	$2$	$1$	$1.038$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(1+i)q^{3}+q^{4}+(-1+2i)q^{5}+\cdots$
130.2.g.c	$130$	$2$	130.g	65.k	$4$	$2$	$1$	$1.038$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(-1-i)q^{3}+q^{4}+(1-2i)q^{5}+\cdots$
130.2.g.d	$130$	$2$	130.g	65.k	$4$	$4$	$2$	$1.038$	$\Q(i, \sqrt{11})$	None		$2$	$0$	$-4$	$2$	$6$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+\cdots$
130.2.g.e	$130$	$2$	130.g	65.k	$4$	$4$	$2$	$1.038$	$\Q(\zeta_{12})$	None		$2$	$0$	$4$	$2$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
130.2.j.a	$130$	$2$	130.j	65.f	$4$	$2$	$1$	$1.038$	$\Q(\sqrt{-1}) $	None		$2$	$1$	$0$	$-4$	$-2$	$-8$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-iq^{2}+(-2+2i)q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots$
130.2.j.b	$130$	$2$	130.j	65.f	$4$	$2$	$1$	$1.038$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$-2$	$-4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+iq^{2}+(-1+i)q^{3}-q^{4}+(-2+i)q^{5}+\cdots$
130.2.j.c	$130$	$2$	130.j	65.f	$4$	$2$	$1$	$1.038$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$0$	$2$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-iq^{2}+(1-i)q^{3}-q^{4}+(2-i)q^{5}+\cdots$
130.2.j.d	$130$	$2$	130.j	65.f	$4$	$4$	$2$	$1.038$	$\Q(i, \sqrt{11})$	None		$2$	$0$	$0$	$2$	$0$	$12$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}-q^{4}+\cdots$
130.2.j.e	$130$	$2$	130.j	65.f	$4$	$4$	$2$	$1.038$	$\Q(\zeta_{12})$	None		$2$	$0$	$0$	$2$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{12}^{3}q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+\cdots$
130.2.l.a	$130$	$2$	130.l	13.e	$6$	$4$	$2$	$1.038$	$\Q(\zeta_{12})$	None		$2$	$0$	$0$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{2}+(1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots$
130.2.l.b	$130$	$2$	130.l	13.e	$6$	$8$	$4$	$1.038$	8.0.22581504.2	None		$2$	$0$	$0$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q-\beta _{1}q^{2}+(\beta _{2}-\beta _{4}-\beta _{7})q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
130.2.m.a	$130$	$2$	130.m	65.l	$6$	$8$	$4$	$1.038$	8.0.$\cdots$.1	None		$2$	$0$	$-4$	$0$	$3$	$5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-1+\beta _{3})q^{2}-\beta _{2}q^{3}-\beta _{3}q^{4}-\beta _{7}q^{5}+\cdots$
130.2.m.b	$130$	$2$	130.m	65.l	$6$	$8$	$4$	$1.038$	8.0.$\cdots$.1	None		$2$	$0$	$4$	$0$	$-3$	$-5$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{3}+\cdots)q^{4}+\cdots$
130.2.n.a	$130$	$2$	130.n	65.n	$6$	$12$	$6$	$1.038$	12.0.$\cdots$.1	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	$q+\beta _{3}q^{2}-\beta _{5}q^{3}+\beta _{8}q^{4}+(-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots$
130.2.p.a	$130$	$2$	130.p	65.t	$12$	$12$	$3$	$1.038$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{6}q^{2}+(\beta _{5}+\beta _{7}+\beta _{8}+\beta _{11})q^{3}+\cdots$
130.2.p.b	$130$	$2$	130.p	65.t	$12$	$16$	$4$	$1.038$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{4})q^{3}+(1+\beta _{8}+\cdots)q^{4}+\cdots$
130.2.s.a	$130$	$2$	130.s	65.o	$12$	$12$	$3$	$1.038$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-6$	$0$	$0$	$6$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}-\beta _{11})q^{3}+(-1+\cdots)q^{4}+\cdots$
130.2.s.b	$130$	$2$	130.s	65.o	$12$	$16$	$4$	$1.038$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$8$	$0$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(1+\beta _{8})q^{2}+(\beta _{2}-\beta _{11})q^{3}+\beta _{8}q^{4}+\cdots$
130.3.f.a	$130$	$3$	130.f	65.g	$4$	$14$	$7$	$3.542$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$-14$	$0$	$-4$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{4})q^{2}+\beta _{1}q^{3}+2\beta _{4}q^{4}+\cdots$
130.3.f.b	$130$	$3$	130.f	65.g	$4$	$14$	$7$	$3.542$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	None		$2$	$0$	$14$	$0$	$2$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{4})q^{2}-\beta _{1}q^{3}+2\beta _{4}q^{4}+\beta _{10}q^{5}+\cdots$
130.3.h.a	$130$	$3$	130.h	65.h	$4$	$2$	$1$	$3.542$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$-2$	$-4$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{2}+(-2+2i)q^{3}-2iq^{4}+\cdots$
130.3.h.b	$130$	$3$	130.h	65.h	$4$	$2$	$1$	$3.542$	$\Q(\sqrt{-1}) $	None		$2$	$0$	$2$	$-4$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{2}+(-2+2i)q^{3}-2iq^{4}+\cdots$
130.3.h.c	$130$	$3$	130.h	65.h	$4$	$12$	$6$	$3.542$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-12$	$4$	$8$	$-12$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{3})q^{2}+\beta _{2}q^{3}-2\beta _{3}q^{4}+\cdots$
130.3.h.d	$130$	$3$	130.h	65.h	$4$	$12$	$6$	$3.542$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$12$	$4$	$-8$	$12$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{3})q^{2}+\beta _{2}q^{3}-2\beta _{3}q^{4}+(-1+\cdots)q^{5}+\cdots$
130.3.i.a	$130$	$3$	130.i	5.c	$4$	$12$	$6$	$3.542$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$-12$	$8$	$-12$	$-16$		$2\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+\beta _{2})q^{2}+(1+\beta _{2}+\beta _{4})q^{3}+\cdots$
130.3.i.b	$130$	$3$	130.i	5.c	$4$	$12$	$6$	$3.542$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None		$2$	$0$	$12$	$0$	$4$	$8$		$2\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{3})q^{2}+\beta _{2}q^{3}-2\beta _{3}q^{4}+(1+\cdots)q^{5}+\cdots$
130.3.k.a	$130$	$3$	130.k	13.d	$4$	$12$	$6$	$3.542$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$-12$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-\beta _{4})q^{2}-\beta _{2}q^{3}+2\beta _{4}q^{4}+\cdots$
130.3.k.b	$130$	$3$	130.k	13.d	$4$	$12$	$6$	$3.542$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		$2$	$0$	$12$	$0$	$0$	$-8$		$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+\beta _{6})q^{2}+\beta _{3}q^{3}+2\beta _{6}q^{4}-\beta _{7}q^{5}+\cdots$
130.3.o.a	$130$	$3$	130.o	13.f	$12$	$16$	$4$	$3.542$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$-8$	$0$	$0$	$16$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{2}-\beta _{11})q^{2}+(-\beta _{3}+\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots$
130.3.o.b	$130$	$3$	130.o	13.f	$12$	$16$	$4$	$3.542$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$2$	$0$	$8$	$0$	$0$	$32$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(1-\beta _{3}-\beta _{6}-\beta _{7})q^{2}+(\beta _{7}+\beta _{10}+\cdots)q^{3}+\cdots$
130.3.q.a	$130$	$3$	130.q	65.q	$12$	$8$	$2$	$3.542$	8.0.5802782976.1	None		$4$	$0$	$-4$	$2$	$24$	$-14$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(\beta _{1}-\beta _{2}+\beta _{5})q^{2}+(-\beta _{2}-\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots$
130.3.q.b	$130$	$3$	130.q	65.q	$12$	$16$	$4$	$3.542$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None		$4$	$0$	$-8$	$-2$	$-28$	$18$		$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	$q+(-1-\beta _{6}-\beta _{9}+\beta _{13})q^{2}+\beta _{15}q^{3}+\cdots$
130.3.q.c	$130$	$3$	130.q	65.q	$12$	$32$	$8$	$3.542$		None		$4$	$0$	$16$	$0$	$12$	$-4$			$\mathrm{SU}(2)[C_{12}]$
130.3.r.a	$130$	$3$	130.r	65.r	$12$	$28$	$7$	$3.542$		None		$2$	$0$	$-14$	$0$	$8$	$4$			$\mathrm{SU}(2)[C_{12}]$
130.3.r.b	$130$	$3$	130.r	65.r	$12$	$28$	$7$	$3.542$		None		$2$	$0$	$14$	$0$	$-8$	$-4$			$\mathrm{SU}(2)[C_{12}]$
130.3.t.a	$130$	$3$	130.t	65.s	$12$	$28$	$7$	$3.542$		None		$2$	$0$	$-14$	$0$	$-2$	$12$			$\mathrm{SU}(2)[C_{12}]$
130.3.t.b	$130$	$3$	130.t	65.s	$12$	$28$	$7$	$3.542$		None		$2$	$0$	$14$	$0$	$4$	$-12$			$\mathrm{SU}(2)[C_{12}]$
130.4.a.a	$130$	$4$	130.a	1.a	$1$	$1$	$1$	$7.670$	$\Q$	None	✓	$1$	$0$	$-2$	$-2$	$5$	$8$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}-2q^{3}+4q^{4}+5q^{5}+4q^{6}+\cdots$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.